Resistors in PARALLEL Configuration

When loads are connected across each other or side by side, so that there is more than one path for the flow of electric current, the resistors are said to be parallel connected. The more the loads are connected in parallel, the lesser the opposition there is to the flow of electric current. The effective resistance is smaller than the smallest resistance value in a circuit.

Below are the rules to be followed in computing the unknown quantities in parallel circuit.

1. The effective resistance (RT) in parallel circuit is smaller than the resistance of the smallest resistive branch.
   1/R_T = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/R_N
2. The total current (IT) is equal to the sum of the individual current flowing through each load / resistive branch.
   I_T + I₁ + I₂ + I₃ + ... + I_N
3. The total voltage (ET) is the same across each branch of the circuit.
   E_T = E₁ = E₂ = E₃ = ... = E_N
4. The total power (PT) is equal to the sum of individual power dissipated by each load.
   P_T + P₁ + P₂ + P₃ + ... + P_N

EXAMPLE 1:

Find the effective resistance of the following circuit.

Resistors in Parallel Configuration

GIVEN: R1 = 50Ω R2 = 150Ω

REQUIRED: RT

Solution:
If there are two loads connected in parallel, use the formula: RT =[ (R1)(R2)] / (R1 + R2)	RT =[ (R1)(R2)]/(R1 + R2) RT =[ (50)(150)]/(50+150) RT =7500 Ohms2/200 ohms RT =37.5 ohms

EXAMPLE 2:

Resistors in Parallel Circuit

GIVEN: R1 = 600Ω R2 = 600Ω R3 = 600Ω R4 = 600Ω

REQUIRED: RT

If there are 2 or more loads with the same resistances are connected parallel, use the formula: RT = R/N where: R is the common resistance value and N is the value of resistors that are parallel connected.

REQUIRED: RT = R/N RT = 600/4 RT = 150 ohms

EXAMPLE 3:

GIVEN: R1 = 200Ω R2 = 400Ω R3 = 600Ω

REQUIRED: RT

SOLUTION: If there are two or more resistors with different resistance value are connected in parallel, use the formula: 1/RT = 1/R1 + 1/R2 + 1/R3 + ... + 1/RN 1/RT = 1/R1 + 1/R2 + 1/R3 + ... + 1/RN 1/RT = 1/200ohms + 1/400ohms + 1/600ohms 1/RT = (6 + 3+ 2) / 1200 ohms 1/RT = 11/1200 ohms RT = 1200 ohms / 11 RT = 109.09 ohms

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